From 7889eeb18131bdbba266d9bf42575dc2108041f1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Fran=C3=A7ois=20Pelletier?= Date: Wed, 29 Jan 2014 21:09:15 -0500 Subject: [PATCH] correction test Wald chapitre 4 --- memoire/chapitre4.tex | 8 ++++---- memoire/gabarit-maitrise.log | 4 ++-- memoire/gabarit-maitrise.pdf | Bin 1004092 -> 1004072 bytes 3 files changed, 6 insertions(+), 6 deletions(-) diff --git a/memoire/chapitre4.tex b/memoire/chapitre4.tex index 8dba1fa..8ca051d 100644 --- a/memoire/chapitre4.tex +++ b/memoire/chapitre4.tex @@ -870,15 +870,15 @@ que la somme de deux variables aléatoires normales l'est aussi: \begin{align} \label{eq:moyennevariancesomme} E\left[\sqrt{T}\left(\hat\theta - \tilde\theta\right) \right] &= - E\left[\sqrt{T}\left(\hat\theta - \theta_0\right) \right] - - E\left[\sqrt{T}\left(\tilde\theta - \theta_0\right) \right]\nonumber\\ + E\left[\sqrt{T}\left(\hat\theta - \theta_0\right) \right] + + E\left[\sqrt{T}\left(\theta_0 - \tilde\theta\right) \right]\nonumber\\ &= 0 - 0 \nonumber\\ &= 0 \\ V\left[\sqrt{T}\left(\hat\theta - \tilde\theta\right) \right] &= V\left[\sqrt{T}\left(\hat\theta - \theta_0\right) \right] + V\left[\sqrt{T}\left(\theta_0 - \tilde\theta\right) \right]\nonumber\\ - &= \left(I+(P-I)\right)\mathcal{J}_0^{-1}\nonumber\\ - &= P\mathcal{J}_0^{-1}. + &= T\left(I+(P-I)\right)\mathcal{J}_0^{-1}\nonumber\\ + &= TP\mathcal{J}_0^{-1}. \end{align} On définit la statistique $\chi^{WALD,1}$, qui a asymptotiquement une diff --git a/memoire/gabarit-maitrise.log b/memoire/gabarit-maitrise.log index 79d8a91..1028fec 100644 --- a/memoire/gabarit-maitrise.log +++ b/memoire/gabarit-maitrise.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2013.12.23) 25 JAN 2014 15:12 +This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2013.11.30) 29 JAN 2014 21:07 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -2261,7 +2261,7 @@ re/texmf/fonts/type1/public/cm-super/sfrm1095.pfb> -Output written on gabarit-maitrise.pdf (155 pages, 1004092 bytes). +Output written on gabarit-maitrise.pdf (155 pages, 1004072 bytes). 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